Question

The point $Q$ is the image of the point $P(1,5)$ about the line $y=x$ and $R$ is the image of the point $Q$ about the line $y=–x$. The circumcenter of the $\Delta PQR$ is

• A. $(5,1)$
• B. $(-5,1)$
• C. $(1,-5)$
• D. $(0,0)$

Answer 1

The correct option is D $(0,0)$

Circumcentre of a triangle is defined as the intersection point of the perpendicular bisectors of the sides


Here $Q$ is the image of $P$ in the line $x=y$
$Q=(5,1)$
Here $R$ is the image of $Q$ in the line $x=-y$
$R=(-1,-5)$
As $x=y$ is perpendicular to the side $PQ$
Similarly $x+y=0$ is perpendicular to the side $QR$
So, $\angle PQR=\frac{\pi }{2}$
The circumcentre will be midpoint of $PR$
$=(0,0)$